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Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. Part 3. Arbitrary-angle perturbations, period doubling of waves

Published online by Cambridge University Press:  13 March 2009

P. Frycz  and
E. Infeld
P. Frycz
Affiliation:
Soltan Institute for Nuclear Studies, Hoza 69, Warsaw 00–681, Poland
E. Infeld
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, U.K.
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Abstract

Nonlinear waves, solutions of the Zakharov–Kuznetsov (ZK) equation for a dilute plasma immersed in a strong magnetic field, are studied numerically. It is found that the most unstable mode rides with the carrier wave and leads to period doubling. Owing to the simplicity of the ZK equation, this and other phenomena, similar to those observed for gravity waves on a water surface, can be fully investigated. Analytical methods are also explored. An expansion in the carrier-wave amplitude leads to good estimates for growth rates, a result so far unobtainable for water waves. This paper can be read independently of parts 1 and 2, but a brief summary of all three parts is given at the end.

Type
Research Article
Information
Journal of Plasma Physics , Volume 41 , Issue 3 , June 1989 , pp. 441 - 446
Copyright
Copyright © Cambridge University Press 1989

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References

REFERENCES

Infeld, E. 1984 J. Plasma Phys. 33, 171.CrossRefGoogle Scholar
Infeld, E. & Frycz, P. 1987 J. Plasma Phys. 37, 97.CrossRefGoogle Scholar
Infeld, E. & Frycz, P. 1988 Nonlinear waves, change of structure and collapse. Physica D (in press).Google Scholar
Laedke, E. W. & Spatschek, K. H. 1982 Phys. Fluids, 25, 985.CrossRefGoogle Scholar
McLean, J. W. 1982 J. Fluid Mech. 114, 331.CrossRefGoogle Scholar
Saffman, P. G. & Yuen, H. C. 1985 Advances in Nonlinear Waves (ed. Debnath, L.), vol. 2, chap. 1. Pitman.Google Scholar
Zakharov, V. E. & Kuznetsov, E. A. 1974 Soviet Phys. JETP, 39, 285.Google Scholar